Matrix Exponential Solutions of First-Order Chemical Networks

Abstract

The matrix exponential method as implemented in MATLAB is demonstrated as a facile tool for solving the time-dependent concentrations of an arbitrary chemically reactive network modelled as a coupled linear system of first-order differential equations. The method is used to verify a 10 species network incorporating experimentally supplied forward rate constants; and a random 11 species network incorporating both forward and backward rate constants as modelled by semiclassical electron transfer theory. Also demonstrated is the matrix exponential solution in exact arithmetic (via Putzer's algorithm and verified by Laplace transforms) for a chain of three species coupled reversibly.